A ramp threshold secret sharing scheme against cheating by substitution attacks
Date
2017
Authors
Nakamura, W.
Yamamoto, H.
Chan, T.
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Conference paper
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Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016, 2017, iss.7840442, pp.340-344
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3rd International Symposium on Information Theory and Its Applications, ISITA 2016 (30 Oct 2016 - 2 Nov 2016 : Monterey, United States)
Abstract
In this paper, we propose a (k, L, n)-threshold ramp secret sharing scheme (SSS) against substitution attacks. This scheme can be applied to a secret S L uniformly distributed over GF(p m ) L , where p is a prime satisfying p ≥ L + 2. We extend Koga and Koyano's analysis based on mutual information of shares for (k, n)-threshold SSSs to (k,L,n) ramp SSSs. The proposed scheme can achieve the minimum sizes of shares and a random number used in encoding. In addition, the success probability of substitution attack for strong (k, L, n) ramp SSSs is less than nearly L times the lower bound if the number of forged shares a satisfies 1 ≤ a ≤ k - 1, and the same holds for weak (k, L,n) ramp SSSs if a satisfies L - a ≤ k - 1.
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Copyright 2016 IEICE.